OF DIALING. 385 



can illuminate the plane of the dial, will (by the rule LECT. 

 H=TLxTD) be twice 6 hours 27 minutes= 12 h. ^^ 

 54 m. The difference of longitude of the planes d and Z 

 was found in the same example to be 36 2* : in time, 

 2 hours 24 minutes ; and the declination of the plane 

 was from the south towards the west. Adding there- 

 fore 2 h. 24 min. to 5 h. 33 m. the earliest sun-rising 

 on a horizontal dial at d, the sum 7 h. 57 min. shews 

 that the morning hours, or the parallel dial at Z, ought 

 to begin at 3 min. before VIII. And to the latest sun- 

 setting at d, which is 6 h. 27 m. adding the same 2 h. 

 24 in. the sum 8 h. 51 m. exceeding 6 h. 16 m. the 

 latest sun-setting at Z, by 35 m. shews that none of the 

 afternoon hour-lines are superfluous. And the 4 h. 

 13 m. from III h. 44 m. the sun-rising at Z to VII h. 

 57 m. the sun-rising at d, belong to the other face of the 

 dial ; that is, to a dial declining 36 from north to east, 

 and inclining 15. 



EXAMPLE III. 

 From the same data to find the sun's azimuth. 



If H, L and D are given, then (by Art. 2. of Rule II.) 

 from H having found the altitude and its complement 

 Z d; and the arc Pd (the distance from the pole) being 

 given : say, As the co-sine of the altitude is to the sine 

 of the distance from the pole, so is the sine of the hour- 

 distance from the meridian to the sine of the azimuth- 

 distance from the meridian. 



Let the latitude be 51 30' north, the declination 

 15 9' south, and the time II h. 24 m. in the afternoon, 

 when the sun begins to illuminate a vertical wall, and it 

 is required to find the position of the wall. 



Then, by the foregoing theorems, the complement of 

 the altitude will be 81* 321 . and P d the distance from 

 25. Cc 



